Abstract: Let be a locally compact semigroup (jointly continuous semigroup operation), the algebra of all bounded regular Borel measures on (with convolution as multiplication), a separated locally convex space and a compact convex subset of . We show that there is a left invariant mean on the space of all bounded left uniformly continuous functions on iff has the following fixed point property: For any bilinear mapping (denoted by ) such that (a) for any , (b) for any , (c) is continuous for any , and is continuous for each when has the topology induced by the seminorms , there is some such that for any .